Abstract
Recent experiments [1] allowed to approach an answer on a fundamental question: what are the size limitations for the existence of superconductivity? In this paper we develop a theoretical investigation of the low temperature behavior of ultrasmall metallic particles with BCS interaction and discrete spectrum of electron levels (characterized by the energy level spacing d). We find that the value of a superconducting gap depends on the level spacing and the electron number parity, being so much smaller in the odd than the even case that these differences should be measurable in current experiments.
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